Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,4,Mod(1,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(132.164278413\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2240.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 5.00000 | 0.962250 | 0.481125 | − | 0.876652i | \(-0.340228\pi\) | ||||
0.481125 | + | 0.876652i | \(0.340228\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | −0.0740741 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −39.0000 | −1.06899 | −0.534497 | − | 0.845170i | \(-0.679499\pi\) | ||||
−0.534497 | + | 0.845170i | \(0.679499\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 19.0000 | 0.405358 | 0.202679 | − | 0.979245i | \(-0.435035\pi\) | ||||
0.202679 | + | 0.979245i | \(0.435035\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 25.0000 | 0.430331 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −37.0000 | −0.527872 | −0.263936 | − | 0.964540i | \(-0.585021\pi\) | ||||
−0.263936 | + | 0.964540i | \(0.585021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.0000 | −0.217341 | −0.108671 | − | 0.994078i | \(-0.534659\pi\) | ||||
−0.108671 | + | 0.994078i | \(0.534659\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 35.0000 | 0.363696 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 90.0000 | 0.815926 | 0.407963 | − | 0.912998i | \(-0.366239\pi\) | ||||
0.407963 | + | 0.912998i | \(0.366239\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −145.000 | −1.03353 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −99.0000 | −0.633925 | −0.316963 | − | 0.948438i | \(-0.602663\pi\) | ||||
−0.316963 | + | 0.948438i | \(0.602663\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 32.0000 | 0.185399 | 0.0926995 | − | 0.995694i | \(-0.470450\pi\) | ||||
0.0926995 | + | 0.995694i | \(0.470450\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −195.000 | −1.02864 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 35.0000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −46.0000 | −0.204388 | −0.102194 | − | 0.994764i | \(-0.532586\pi\) | ||||
−0.102194 | + | 0.994764i | \(0.532586\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 95.0000 | 0.390056 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −248.000 | −0.944661 | −0.472330 | − | 0.881422i | \(-0.656587\pi\) | ||||
−0.472330 | + | 0.881422i | \(0.656587\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 178.000 | 0.631273 | 0.315637 | − | 0.948880i | \(-0.397782\pi\) | ||||
0.315637 | + | 0.948880i | \(0.397782\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.0000 | −0.0331269 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −429.000 | −1.33141 | −0.665703 | − | 0.746217i | \(-0.731868\pi\) | ||||
−0.665703 | + | 0.746217i | \(0.731868\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −185.000 | −0.507945 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 652.000 | 1.68979 | 0.844897 | − | 0.534929i | \(-0.179662\pi\) | ||||
0.844897 | + | 0.534929i | \(0.179662\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −195.000 | −0.478069 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −90.0000 | −0.209137 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 40.0000 | 0.0882637 | 0.0441318 | − | 0.999026i | \(-0.485948\pi\) | ||||
0.0441318 | + | 0.999026i | \(0.485948\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 36.0000 | 0.0755627 | 0.0377814 | − | 0.999286i | \(-0.487971\pi\) | ||||
0.0377814 | + | 0.999286i | \(0.487971\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −14.0000 | −0.0279974 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 95.0000 | 0.181282 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −348.000 | −0.634552 | −0.317276 | − | 0.948333i | \(-0.602768\pi\) | ||||
−0.317276 | + | 0.948333i | \(0.602768\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 450.000 | 0.785125 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −72.0000 | −0.120350 | −0.0601748 | − | 0.998188i | \(-0.519166\pi\) | ||||
−0.0601748 | + | 0.998188i | \(0.519166\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1190.00 | −1.90793 | −0.953966 | − | 0.299916i | \(-0.903041\pi\) | ||||
−0.953966 | + | 0.299916i | \(0.903041\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 125.000 | 0.192450 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −273.000 | −0.404042 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −699.000 | −0.995489 | −0.497745 | − | 0.867324i | \(-0.665838\pi\) | ||||
−0.497745 | + | 0.867324i | \(0.665838\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −671.000 | −0.920439 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −116.000 | −0.153405 | −0.0767027 | − | 0.997054i | \(-0.524439\pi\) | ||||
−0.0767027 | + | 0.997054i | \(0.524439\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −185.000 | −0.236071 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −495.000 | −0.609995 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −704.000 | −0.838470 | −0.419235 | − | 0.907878i | \(-0.637702\pi\) | ||||
−0.419235 | + | 0.907878i | \(0.637702\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 133.000 | 0.153211 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 160.000 | 0.178400 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −90.0000 | −0.0971979 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 223.000 | 0.233425 | 0.116712 | − | 0.993166i | \(-0.462764\pi\) | ||||
0.116712 | + | 0.993166i | \(0.462764\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 78.0000 | 0.0791848 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −522.000 | −0.514267 | −0.257133 | − | 0.966376i | \(-0.582778\pi\) | ||||
−0.257133 | + | 0.966376i | \(0.582778\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1697.00 | −1.62340 | −0.811701 | − | 0.584073i | \(-0.801458\pi\) | ||||
−0.811701 | + | 0.584073i | \(0.801458\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 175.000 | 0.162650 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 246.000 | 0.222259 | 0.111130 | − | 0.993806i | \(-0.464553\pi\) | ||||
0.111130 | + | 0.993806i | \(0.464553\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −345.000 | −0.303165 | −0.151583 | − | 0.988445i | \(-0.548437\pi\) | ||||
−0.151583 | + | 0.988445i | \(0.548437\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −230.000 | −0.196672 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 186.000 | 0.154844 | 0.0774222 | − | 0.996998i | \(-0.475331\pi\) | ||||
0.0774222 | + | 0.996998i | \(0.475331\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 450.000 | 0.364893 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −38.0000 | −0.0300265 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −259.000 | −0.199517 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 190.000 | 0.142750 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1240.00 | −0.909000 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2344.00 | −1.63777 | −0.818883 | − | 0.573960i | \(-0.805406\pi\) | ||||
−0.818883 | + | 0.573960i | \(0.805406\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 890.000 | 0.607443 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 958.000 | 0.638938 | 0.319469 | − | 0.947597i | \(-0.396496\pi\) | ||||
0.319469 | + | 0.947597i | \(0.396496\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −126.000 | −0.0821473 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −725.000 | −0.462208 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 768.000 | 0.478939 | 0.239470 | − | 0.970904i | \(-0.423026\pi\) | ||||
0.239470 | + | 0.970904i | \(0.423026\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −122.000 | −0.0744454 | −0.0372227 | − | 0.999307i | \(-0.511851\pi\) | ||||
−0.0372227 | + | 0.999307i | \(0.511851\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2145.00 | −1.28115 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −741.000 | −0.433325 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −495.000 | −0.283500 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 245.000 | 0.137464 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 166.000 | 0.0912701 | 0.0456351 | − | 0.998958i | \(-0.485469\pi\) | ||||
0.0456351 | + | 0.998958i | \(0.485469\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1725.00 | 0.929659 | 0.464830 | − | 0.885400i | \(-0.346116\pi\) | ||||
0.464830 | + | 0.885400i | \(0.346116\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 74.0000 | 0.0391016 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 160.000 | 0.0829130 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3686.00 | −1.87373 | −0.936863 | − | 0.349698i | \(-0.886284\pi\) | ||||
−0.936863 | + | 0.349698i | \(0.886284\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3260.00 | 1.62601 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 630.000 | 0.308391 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2594.00 | 1.24649 | 0.623245 | − | 0.782027i | \(-0.285814\pi\) | ||||
0.623245 | + | 0.782027i | \(0.285814\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −975.000 | −0.460022 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1457.00 | −0.675126 | −0.337563 | − | 0.941303i | \(-0.609603\pi\) | ||||
−0.337563 | + | 0.941303i | \(0.609603\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1836.00 | −0.835685 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 36.0000 | 0.0160993 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3241.00 | 1.42433 | 0.712164 | − | 0.702013i | \(-0.247715\pi\) | ||||
0.712164 | + | 0.702013i | \(0.247715\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 175.000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 200.000 | 0.0849318 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4596.00 | −1.91911 | −0.959556 | − | 0.281517i | \(-0.909163\pi\) | ||||
−0.959556 | + | 0.281517i | \(0.909163\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1140.00 | 0.468152 | 0.234076 | − | 0.972218i | \(-0.424794\pi\) | ||||
0.234076 | + | 0.972218i | \(0.424794\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 180.000 | 0.0727103 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −230.000 | −0.0914051 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1443.00 | 0.564292 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1015.00 | −0.390637 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4131.00 | 1.56497 | 0.782483 | − | 0.622671i | \(-0.213953\pi\) | ||||
0.782483 | + | 0.622671i | \(0.213953\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2792.00 | −1.04131 | −0.520654 | − | 0.853768i | \(-0.674312\pi\) | ||||
−0.520654 | + | 0.853768i | \(0.674312\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 475.000 | 0.174438 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2692.00 | −0.973589 | −0.486795 | − | 0.873516i | \(-0.661834\pi\) | ||||
−0.486795 | + | 0.873516i | \(0.661834\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2640.00 | 0.940425 | 0.470213 | − | 0.882553i | \(-0.344177\pi\) | ||||
0.470213 | + | 0.882553i | \(0.344177\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1740.00 | −0.610598 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −693.000 | −0.239601 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1240.00 | −0.422465 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −180.000 | −0.0604390 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 702.000 | 0.232337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 327.000 | 0.106690 | 0.0533450 | − | 0.998576i | \(-0.483012\pi\) | ||||
0.0533450 | + | 0.998576i | \(0.483012\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −360.000 | −0.115807 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 890.000 | 0.282314 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 224.000 | 0.0700742 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5950.00 | −1.83591 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −703.000 | −0.213977 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4665.00 | −1.40086 | −0.700429 | − | 0.713722i | \(-0.747008\pi\) | ||||
−0.700429 | + | 0.713722i | \(0.747008\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −50.0000 | −0.0148148 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1071.00 | −0.313149 | −0.156574 | − | 0.987666i | \(-0.550045\pi\) | ||||
−0.156574 | + | 0.987666i | \(0.550045\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3920.00 | 1.13118 | 0.565591 | − | 0.824686i | \(-0.308648\pi\) | ||||
0.565591 | + | 0.824686i | \(0.308648\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1365.00 | −0.388790 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2616.00 | −0.735536 | −0.367768 | − | 0.929918i | \(-0.619878\pi\) | ||||
−0.367768 | + | 0.929918i | \(0.619878\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2145.00 | −0.595423 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3495.00 | −0.957910 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6913.00 | 1.87098 | 0.935491 | − | 0.353350i | \(-0.114958\pi\) | ||||
0.935491 | + | 0.353350i | \(0.114958\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2690.00 | 0.718996 | 0.359498 | − | 0.933146i | \(-0.382948\pi\) | ||||
0.359498 | + | 0.933146i | \(0.382948\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 560.000 | 0.147835 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 245.000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −342.000 | −0.0881010 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −580.000 | −0.147614 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3034.00 | 0.762966 | 0.381483 | − | 0.924376i | \(-0.375414\pi\) | ||||
0.381483 | + | 0.924376i | \(0.375414\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3510.00 | −0.872221 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −925.000 | −0.227160 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2266.00 | −0.549997 | −0.274998 | − | 0.961445i | \(-0.588677\pi\) | ||||
−0.274998 | + | 0.961445i | \(0.588677\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −322.000 | −0.0772514 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 198.000 | 0.0469574 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7058.00 | 1.65481 | 0.827405 | − | 0.561606i | \(-0.189816\pi\) | ||||
0.827405 | + | 0.561606i | \(0.189816\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3260.00 | 0.755699 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3520.00 | −0.806818 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3474.00 | −0.787411 | −0.393705 | − | 0.919237i | \(-0.628807\pi\) | ||||
−0.393705 | + | 0.919237i | \(0.628807\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0000 | 0.00448308 | 0.00224154 | − | 0.999997i | \(-0.499286\pi\) | ||||
0.00224154 | + | 0.999997i | \(0.499286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 665.000 | 0.147427 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −975.000 | −0.213799 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4186.00 | 0.907987 | 0.453993 | − | 0.891005i | \(-0.349999\pi\) | ||||
0.453993 | + | 0.891005i | \(0.349999\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −64.0000 | −0.0137333 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7221.00 | −1.53298 | −0.766492 | − | 0.642253i | \(-0.778000\pi\) | ||||
−0.766492 | + | 0.642253i | \(0.778000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.0000 | 0.00483112 | 0.00241556 | − | 0.999997i | \(-0.499231\pi\) | ||||
0.00241556 | + | 0.999997i | \(0.499231\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −450.000 | −0.0935288 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1736.00 | −0.357048 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3544.00 | −0.721352 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1115.00 | 0.224613 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −139.000 | −0.0277149 | −0.0138575 | − | 0.999904i | \(-0.504411\pi\) | ||||
−0.0138575 | + | 0.999904i | \(0.504411\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 200.000 | 0.0394727 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5655.00 | 1.10484 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1710.00 | 0.330742 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1246.00 | 0.238599 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2610.00 | −0.494853 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 180.000 | 0.0337927 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6759.00 | 1.25654 | 0.628268 | − | 0.777997i | \(-0.283764\pi\) | ||||
0.628268 | + | 0.777997i | \(0.283764\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8485.00 | −1.56212 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1038.00 | −0.189259 | −0.0946295 | − | 0.995513i | \(-0.530167\pi\) | ||||
−0.0946295 | + | 0.995513i | \(0.530167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9507.00 | −1.71683 | −0.858414 | − | 0.512957i | \(-0.828550\pi\) | ||||
−0.858414 | + | 0.512957i | \(0.828550\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −70.0000 | −0.0125208 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1290.00 | 0.228560 | 0.114280 | − | 0.993449i | \(-0.463544\pi\) | ||||
0.114280 | + | 0.993449i | \(0.463544\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3861.00 | 0.677663 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1230.00 | 0.213869 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 666.000 | 0.114728 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 475.000 | 0.0810716 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1725.00 | −0.291721 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3003.00 | −0.503224 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5404.00 | −0.897374 | −0.448687 | − | 0.893689i | \(-0.648108\pi\) | ||||
−0.448687 | + | 0.893689i | \(0.648108\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 92.0000 | 0.0151398 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1740.00 | −0.283780 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3094.00 | 0.500121 | 0.250061 | − | 0.968230i | \(-0.419549\pi\) | ||||
0.250061 | + | 0.968230i | \(0.419549\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 930.000 | 0.148999 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1248.00 | −0.198191 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2250.00 | 0.351119 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1486.00 | −0.229892 | −0.114946 | − | 0.993372i | \(-0.536670\pi\) | ||||
−0.114946 | + | 0.993372i | \(0.536670\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6630.00 | −1.01689 | −0.508447 | − | 0.861093i | \(-0.669780\pi\) | ||||
−0.508447 | + | 0.861093i | \(0.669780\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2755.00 | −0.418949 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5417.00 | −0.816764 | −0.408382 | − | 0.912811i | \(-0.633907\pi\) | ||||
−0.408382 | + | 0.912811i | \(0.633907\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −360.000 | −0.0538220 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1295.00 | −0.191985 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9200.00 | 1.35253 | 0.676264 | − | 0.736660i | \(-0.263598\pi\) | ||||
0.676264 | + | 0.736660i | \(0.263598\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6535.00 | −0.952763 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 950.000 | 0.137361 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5950.00 | −0.853253 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4157.00 | −0.591263 | −0.295632 | − | 0.955302i | \(-0.595530\pi\) | ||||
−0.295632 | + | 0.955302i | \(0.595530\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 496.000 | 0.0699749 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4564.00 | 0.638682 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8592.00 | −1.19270 | −0.596350 | − | 0.802725i | \(-0.703383\pi\) | ||||
−0.596350 | + | 0.802725i | \(0.703383\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 625.000 | 0.0860663 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1881.00 | −0.256967 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2084.00 | 0.282448 | 0.141224 | − | 0.989978i | \(-0.454896\pi\) | ||||
0.141224 | + | 0.989978i | \(0.454896\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11720.0 | −1.57594 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9292.00 | 1.23968 | 0.619842 | − | 0.784727i | \(-0.287197\pi\) | ||||
0.619842 | + | 0.784727i | \(0.287197\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1365.00 | −0.180693 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −356.000 | −0.0467610 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1723.00 | 0.224575 | 0.112287 | − | 0.993676i | \(-0.464182\pi\) | ||||
0.112287 | + | 0.993676i | \(0.464182\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3330.00 | −0.430704 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4790.00 | 0.614818 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3495.00 | −0.445196 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3767.00 | −0.476222 | −0.238111 | − | 0.971238i | \(-0.576528\pi\) | ||||
−0.238111 | + | 0.971238i | \(0.576528\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −630.000 | −0.0790462 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14967.0 | −1.86388 | −0.931941 | − | 0.362611i | \(-0.881885\pi\) | ||||
−0.931941 | + | 0.362611i | \(0.881885\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 608.000 | 0.0751529 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3355.00 | −0.411633 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1794.00 | 0.218490 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11374.0 | 1.37508 | 0.687540 | − | 0.726146i | \(-0.258690\pi\) | ||||
0.687540 | + | 0.726146i | \(0.258690\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3840.00 | 0.460859 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 280.000 | 0.0333605 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −580.000 | −0.0686050 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −610.000 | −0.0716351 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14076.0 | 1.64119 | 0.820594 | − | 0.571512i | \(-0.193643\pi\) | ||||
0.820594 | + | 0.571512i | \(0.193643\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3769.00 | −0.436318 | −0.218159 | − | 0.975913i | \(-0.570005\pi\) | ||||
−0.218159 | + | 0.975913i | \(0.570005\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 858.000 | 0.0986227 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −925.000 | −0.105574 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 252.000 | 0.0285600 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3705.00 | −0.416968 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7423.00 | 0.829590 | 0.414795 | − | 0.909915i | \(-0.363853\pi\) | ||||
0.414795 | + | 0.909915i | \(0.363853\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −670.000 | −0.0743606 | −0.0371803 | − | 0.999309i | \(-0.511838\pi\) | ||||
−0.0371803 | + | 0.999309i | \(0.511838\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2475.00 | −0.272798 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1620.00 | −0.177334 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6466.00 | −0.702973 | −0.351487 | − | 0.936193i | \(-0.614324\pi\) | ||||
−0.351487 | + | 0.936193i | \(0.614324\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −98.0000 | −0.0105820 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14618.0 | 1.56777 | 0.783885 | − | 0.620906i | \(-0.213235\pi\) | ||||
0.783885 | + | 0.620906i | \(0.213235\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3520.00 | −0.374975 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 830.000 | 0.0878247 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7551.00 | 0.793661 | 0.396830 | − | 0.917892i | \(-0.370110\pi\) | ||||
0.396830 | + | 0.917892i | \(0.370110\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9672.00 | 1.00984 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8625.00 | 0.894565 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 665.000 | 0.0685180 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14076.0 | −1.44080 | −0.720402 | − | 0.693557i | \(-0.756043\pi\) | ||||
−0.720402 | + | 0.693557i | \(0.756043\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5365.00 | 0.545570 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18360.0 | 1.85490 | 0.927452 | − | 0.373943i | \(-0.121994\pi\) | ||||
0.927452 | + | 0.373943i | \(0.121994\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2812.00 | −0.282256 | −0.141128 | − | 0.989991i | \(-0.545073\pi\) | ||||
−0.141128 | + | 0.989991i | \(0.545073\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 800.000 | 0.0797830 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2619.00 | 0.259514 | 0.129757 | − | 0.991546i | \(-0.458580\pi\) | ||||
0.129757 | + | 0.991546i | \(0.458580\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2436.00 | −0.239838 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18430.0 | −1.80299 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6942.00 | −0.674828 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −450.000 | −0.0434682 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1304.00 | −0.125170 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7546.00 | 0.719803 | 0.359901 | − | 0.932990i | \(-0.382810\pi\) | ||||
0.359901 | + | 0.932990i | \(0.382810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −874.000 | −0.0828502 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3150.00 | 0.296749 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1115.00 | 0.104391 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9398.00 | −0.874464 | −0.437232 | − | 0.899349i | \(-0.644041\pi\) | ||||
−0.437232 | + | 0.899349i | \(0.644041\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12970.0 | 1.19943 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5397.00 | −0.496055 | −0.248028 | − | 0.968753i | \(-0.579782\pi\) | ||||
−0.248028 | + | 0.968753i | \(0.579782\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3663.00 | 0.334631 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 390.000 | 0.0354125 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −504.000 | −0.0454879 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11669.0 | 1.04685 | 0.523423 | − | 0.852073i | \(-0.324655\pi\) | ||||
0.523423 | + | 0.852073i | \(0.324655\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7285.00 | −0.649640 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4055.00 | −0.359450 | −0.179725 | − | 0.983717i | \(-0.557521\pi\) | ||||
−0.179725 | + | 0.983717i | \(0.557521\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2610.00 | −0.229987 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9180.00 | −0.804138 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12026.0 | −1.04724 | −0.523618 | − | 0.851953i | \(-0.675418\pi\) | ||||
−0.523618 | + | 0.851953i | \(0.675418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8330.00 | −0.721130 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2610.00 | 0.224628 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8485.00 | −0.726007 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16731.0 | 1.42327 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16205.0 | 1.37056 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17622.0 | −1.48183 | −0.740915 | − | 0.671598i | \(-0.765608\pi\) | ||||
−0.740915 | + | 0.671598i | \(0.765608\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14684.0 | 1.22770 | 0.613849 | − | 0.789423i | \(-0.289620\pi\) | ||||
0.613849 | + | 0.789423i | \(0.289620\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 875.000 | 0.0727393 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1184.00 | −0.0978669 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4067.00 | −0.334265 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −80.0000 | −0.00653805 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4712.00 | −0.382926 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1230.00 | 0.0993973 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22980.0 | −1.84667 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1911.00 | −0.152714 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5741.00 | 0.456238 | 0.228119 | − | 0.973633i | \(-0.426742\pi\) | ||||
0.228119 | + | 0.973633i | \(0.426742\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5700.00 | 0.450480 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1725.00 | −0.135580 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9268.00 | −0.724444 | −0.362222 | − | 0.932092i | \(-0.617982\pi\) | ||||
−0.362222 | + | 0.932092i | \(0.617982\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −72.0000 | −0.00559724 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1782.00 | 0.137778 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4893.00 | −0.376260 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1150.00 | −0.0879546 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23112.0 | 1.75815 | 0.879073 | − | 0.476688i | \(-0.158163\pi\) | ||||
0.879073 | + | 0.476688i | \(0.158163\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3382.00 | 0.255892 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7215.00 | 0.542990 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13284.0 | −0.994412 | −0.497206 | − | 0.867633i | \(-0.665641\pi\) | ||||
−0.497206 | + | 0.867633i | \(0.665641\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 930.000 | 0.0692485 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4697.00 | −0.347893 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10446.0 | −0.769629 | −0.384815 | − | 0.922994i | \(-0.625735\pi\) | ||||
−0.384815 | + | 0.922994i | \(0.625735\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2252.00 | −0.165050 | −0.0825248 | − | 0.996589i | \(-0.526298\pi\) | ||||
−0.0825248 | + | 0.996589i | \(0.526298\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20655.0 | 1.50589 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2250.00 | 0.163185 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4457.00 | 0.321573 | 0.160786 | − | 0.986989i | \(-0.448597\pi\) | ||||
0.160786 | + | 0.986989i | \(0.448597\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13960.0 | −1.00200 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −812.000 | −0.0579818 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25428.0 | −1.80638 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −190.000 | −0.0134283 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25048.0 | −1.76123 | −0.880615 | − | 0.473833i | \(-0.842870\pi\) | ||||
−0.880615 | + | 0.473833i | \(0.842870\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −576.000 | −0.0402948 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13460.0 | −0.936837 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 177.000 | 0.0122572 | 0.00612860 | − | 0.999981i | \(-0.498049\pi\) | ||||
0.00612860 | + | 0.999981i | \(0.498049\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1295.00 | −0.0892266 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13200.0 | 0.904925 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9009.00 | −0.614520 | −0.307260 | − | 0.951626i | \(-0.599412\pi\) | ||||
−0.307260 | + | 0.951626i | \(0.599412\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25794.0 | −1.75068 | −0.875340 | − | 0.483507i | \(-0.839363\pi\) | ||||
−0.875340 | + | 0.483507i | \(0.839363\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 696.000 | 0.0470038 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 950.000 | 0.0638397 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4319.00 | −0.288802 | −0.144401 | − | 0.989519i | \(-0.546126\pi\) | ||||
−0.144401 | + | 0.989519i | \(0.546126\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3465.00 | −0.230556 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8151.00 | −0.539696 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15134.0 | 0.997156 | 0.498578 | − | 0.866845i | \(-0.333856\pi\) | ||||
0.498578 | + | 0.866845i | \(0.333856\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6200.00 | −0.406517 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8394.00 | 0.547698 | 0.273849 | − | 0.961773i | \(-0.411703\pi\) | ||||
0.273849 | + | 0.961773i | \(0.411703\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1658.00 | −0.107659 | −0.0538293 | − | 0.998550i | \(-0.517143\pi\) | ||||
−0.0538293 | + | 0.998550i | \(0.517143\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13050.0 | −0.843283 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4928.00 | −0.316912 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3510.00 | 0.223566 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1702.00 | 0.107891 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8071.00 | 0.509194 | 0.254597 | − | 0.967047i | \(-0.418057\pi\) | ||||
0.254597 | + | 0.967047i | \(0.418057\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1635.00 | 0.102663 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11720.0 | −0.732432 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 931.000 | 0.0579083 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 144.000 | 0.00891479 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28130.0 | 1.73334 | 0.866668 | − | 0.498886i | \(-0.166257\pi\) | ||||
0.866668 | + | 0.498886i | \(0.166257\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2693.00 | 0.165166 | 0.0825829 | − | 0.996584i | \(-0.473683\pi\) | ||||
0.0825829 | + | 0.996584i | \(0.473683\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4450.00 | 0.271657 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1376.00 | −0.0836107 | −0.0418054 | − | 0.999126i | \(-0.513311\pi\) | ||||
−0.0418054 | + | 0.999126i | \(0.513311\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1560.00 | −0.0943534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1120.00 | 0.0674290 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30342.0 | −1.81834 | −0.909169 | − | 0.416428i | \(-0.863282\pi\) | ||||
−0.909169 | + | 0.416428i | \(0.863282\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4790.00 | 0.285742 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2380.00 | 0.141328 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15163.0 | −0.896307 | −0.448154 | − | 0.893957i | \(-0.647918\pi\) | ||||
−0.448154 | + | 0.893957i | \(0.647918\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5688.00 | 0.334701 | 0.167351 | − | 0.985897i | \(-0.446479\pi\) | ||||
0.167351 | + | 0.985897i | \(0.446479\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3515.00 | −0.205899 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −630.000 | −0.0367374 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8910.00 | −0.517236 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23325.0 | −1.34798 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1404.00 | −0.0807762 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21488.0 | 1.23076 | 0.615380 | − | 0.788231i | \(-0.289003\pi\) | ||||
0.615380 | + | 0.788231i | \(0.289003\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3625.00 | −0.206706 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16453.0 | −0.934033 | −0.467016 | − | 0.884249i | \(-0.654671\pi\) | ||||
−0.467016 | + | 0.884249i | \(0.654671\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1561.00 | 0.0882263 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5355.00 | −0.301328 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3372.00 | −0.188911 | −0.0944553 | − | 0.995529i | \(-0.530111\pi\) | ||||
−0.0944553 | + | 0.995529i | \(0.530111\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3840.00 | 0.214188 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19600.0 | 1.08848 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12388.0 | 0.684971 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14172.0 | 0.780215 | 0.390107 | − | 0.920769i | \(-0.372438\pi\) | ||||
0.390107 | + | 0.920769i | \(0.372438\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 546.000 | 0.0299290 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −610.000 | −0.0332930 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9176.00 | 0.498660 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13080.0 | −0.707770 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30663.0 | −1.65210 | −0.826052 | − | 0.563593i | \(-0.809419\pi\) | ||||
−0.826052 | + | 0.563593i | \(0.809419\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 828.000 | 0.0444219 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10725.0 | −0.572946 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3654.00 | −0.194375 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14485.0 | 0.767272 | 0.383636 | − | 0.923484i | \(-0.374672\pi\) | ||||
0.383636 | + | 0.923484i | \(0.374672\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1398.00 | 0.0737399 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2880.00 | 0.151272 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3705.00 | −0.193789 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 34565.0 | 1.80035 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8818.00 | 0.457380 | 0.228690 | − | 0.973499i | \(-0.426556\pi\) | ||||
0.228690 | + | 0.973499i | \(0.426556\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11879.0 | −0.613588 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13450.0 | 0.691855 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2475.00 | −0.126785 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11408.0 | 0.581980 | 0.290990 | − | 0.956726i | \(-0.406015\pi\) | ||||
0.290990 | + | 0.956726i | \(0.406015\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20917.0 | 1.06269 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6586.00 | −0.333231 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15233.0 | −0.767590 | −0.383795 | − | 0.923418i | \(-0.625383\pi\) | ||||
−0.383795 | + | 0.923418i | \(0.625383\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1225.00 | 0.0614759 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13572.0 | 0.678332 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32113.0 | 1.59851 | 0.799253 | − | 0.600995i | \(-0.205229\pi\) | ||||
0.799253 | + | 0.600995i | \(0.205229\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1710.00 | −0.0847752 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4596.00 | −0.226933 | −0.113466 | − | 0.993542i | \(-0.536195\pi\) | ||||
−0.113466 | + | 0.993542i | \(0.536195\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 830.000 | 0.0408172 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 232.000 | 0.0113634 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1722.00 | 0.0840060 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15893.0 | 0.772229 | 0.386114 | − | 0.922451i | \(-0.373817\pi\) | ||||
0.386114 | + | 0.922451i | \(0.373817\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15170.0 | 0.734164 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8625.00 | 0.415756 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15336.0 | −0.736323 | −0.368161 | − | 0.929762i | \(-0.620013\pi\) | ||||
−0.368161 | + | 0.929762i | \(0.620013\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17550.0 | −0.839295 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33010.0 | 1.57242 | 0.786210 | − | 0.617959i | \(-0.212040\pi\) | ||||
0.786210 | + | 0.617959i | \(0.212040\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2415.00 | −0.114586 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 370.000 | 0.0174868 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 760.000 | 0.0357784 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30982.0 | 1.45285 | 0.726424 | − | 0.687247i | \(-0.241181\pi\) | ||||
0.726424 | + | 0.687247i | \(0.241181\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11330.0 | −0.529235 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5915.00 | 0.275223 | 0.137612 | − | 0.990486i | \(-0.456057\pi\) | ||||
0.137612 | + | 0.990486i | \(0.456057\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 800.000 | 0.0370798 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1610.00 | −0.0743352 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4464.00 | 0.205314 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2808.00 | 0.128653 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14355.0 | 0.655180 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18430.0 | −0.837955 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24615.0 | −1.11490 | −0.557452 | − | 0.830209i | \(-0.688221\pi\) | ||||
−0.557452 | + | 0.830209i | \(0.688221\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 35290.0 | 1.59234 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1302.00 | 0.0585257 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 684.000 | 0.0306300 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16300.0 | 0.727172 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6055.00 | −0.269108 | −0.134554 | − | 0.990906i | \(-0.542960\pi\) | ||||
−0.134554 | + | 0.990906i | \(0.542960\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15873.0 | 0.702811 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1408.00 | 0.0621089 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 46410.0 | 2.03957 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3150.00 | 0.137917 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17370.0 | −0.757686 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27809.0 | 1.20854 | 0.604272 | − | 0.796778i | \(-0.293464\pi\) | ||||
0.604272 | + | 0.796778i | \(0.293464\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18654.0 | −0.807683 | −0.403841 | − | 0.914829i | \(-0.632325\pi\) | ||||
−0.403841 | + | 0.914829i | \(0.632325\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 100.000 | 0.00431384 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12970.0 | 0.557447 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3204.00 | −0.137202 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −266.000 | −0.0113490 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27285.0 | −1.15987 | −0.579935 | − | 0.814663i | \(-0.696922\pi\) | ||||
−0.579935 | + | 0.814663i | \(0.696922\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18592.0 | −0.787456 | −0.393728 | − | 0.919227i | \(-0.628815\pi\) | ||||
−0.393728 | + | 0.919227i | \(0.628815\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4875.00 | −0.205728 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37146.0 | −1.56190 | −0.780951 | − | 0.624592i | \(-0.785265\pi\) | ||||
−0.780951 | + | 0.624592i | \(0.785265\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11024.0 | −0.461857 | −0.230928 | − | 0.972971i | \(-0.574176\pi\) | ||||
−0.230928 | + | 0.972971i | \(0.574176\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20930.0 | 0.873711 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1813.00 | −0.0754102 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7285.00 | −0.301926 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4640.00 | −0.191615 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42858.0 | −1.76355 | −0.881777 | − | 0.471666i | \(-0.843653\pi\) | ||||
−0.881777 | + | 0.471666i | \(0.843653\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14588.0 | −0.598139 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −36105.0 | −1.47512 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9180.00 | −0.373730 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1330.00 | 0.0539544 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 115.000 | 0.00464875 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4140.00 | −0.166765 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31522.0 | 1.26529 | 0.632645 | − | 0.774442i | \(-0.281969\pi\) | ||||
0.632645 | + | 0.774442i | \(0.281969\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 180.000 | 0.00719985 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37026.0 | 1.47583 | 0.737914 | − | 0.674895i | \(-0.235811\pi\) | ||||
0.737914 | + | 0.674895i | \(0.235811\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34380.0 | 1.36558 | 0.682788 | − | 0.730616i | \(-0.260767\pi\) | ||||
0.682788 | + | 0.730616i | \(0.260767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8680.00 | −0.343570 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29172.0 | 1.15067 | 0.575334 | − | 0.817919i | \(-0.304872\pi\) | ||||
0.575334 | + | 0.817919i | \(0.304872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16205.0 | 0.636979 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17720.0 | −0.694121 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27261.0 | 1.06417 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6612.00 | −0.257221 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −446.000 | −0.0172907 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 875.000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18178.0 | 0.699917 | 0.349959 | − | 0.936765i | \(-0.386196\pi\) | ||||
0.349959 | + | 0.936765i | \(0.386196\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −695.000 | −0.0266687 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2608.00 | 0.0997341 | 0.0498671 | − | 0.998756i | \(-0.484120\pi\) | ||||
0.0498671 | + | 0.998756i | \(0.484120\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26880.0 | 1.02444 | 0.512222 | − | 0.858853i | \(-0.328823\pi\) | ||||
0.512222 | + | 0.858853i | \(0.328823\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1000.00 | 0.0379826 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31208.0 | −1.18136 | −0.590678 | − | 0.806908i | \(-0.701139\pi\) | ||||
−0.590678 | + | 0.806908i | \(0.701139\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16408.0 | −0.619018 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26169.0 | 0.983944 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7722.00 | 0.289369 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22980.0 | −0.858253 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8550.00 | 0.318257 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3168.00 | −0.117529 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24124.0 | −0.891994 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6230.00 | 0.229592 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5700.00 | 0.209364 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21494.0 | 0.786876 | 0.393438 | − | 0.919351i | \(-0.371286\pi\) | ||||
0.393438 | + | 0.919351i | \(0.371286\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1044.00 | 0.0380938 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3704.00 | −0.134708 | −0.0673540 | − | 0.997729i | \(-0.521456\pi\) | ||||
−0.0673540 | + | 0.997729i | \(0.521456\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4524.00 | 0.163990 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 900.000 | 0.0325170 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6706.00 | 0.241496 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16185.0 | 0.580951 | 0.290475 | − | 0.956882i | \(-0.406187\pi\) | ||||
0.290475 | + | 0.956882i | \(0.406187\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 33795.0 | 1.20910 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1368.00 | −0.0487847 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1150.00 | −0.0408776 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3394.00 | 0.120252 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8500.00 | 0.300189 | 0.150095 | − | 0.988672i | \(-0.452042\pi\) | ||||
0.150095 | + | 0.988672i | \(0.452042\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −882.000 | −0.0310487 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5190.00 | −0.182115 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7215.00 | 0.252359 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33415.0 | 1.16502 | 0.582508 | − | 0.812825i | \(-0.302071\pi\) | ||||
0.582508 | + | 0.812825i | \(0.302071\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −47535.0 | −1.65202 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25884.0 | 0.896700 | 0.448350 | − | 0.893858i | \(-0.352012\pi\) | ||||
0.448350 | + | 0.893858i | \(0.352012\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22320.0 | −0.770773 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5075.00 | −0.174698 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26404.0 | 0.906035 | 0.453017 | − | 0.891502i | \(-0.350348\pi\) | ||||
0.453017 | + | 0.891502i | \(0.350348\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22610.0 | −0.773395 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6450.00 | 0.219932 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21068.0 | −0.716117 | −0.358058 | − | 0.933699i | \(-0.616561\pi\) | ||||
−0.358058 | + | 0.933699i | \(0.616561\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20655.0 | 0.699874 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19305.0 | 0.652082 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5376.00 | 0.181022 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28767.0 | −0.965627 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −492.000 | −0.0164636 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13960.0 | −0.465687 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −298.000 | −0.00991007 | −0.00495503 | − | 0.999988i | \(-0.501577\pi\) | ||||
−0.00495503 | + | 0.999988i | \(0.501577\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3330.00 | 0.110397 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8972.00 | −0.296524 | −0.148262 | − | 0.988948i | \(-0.547368\pi\) | ||||
−0.148262 | + | 0.988948i | \(0.547368\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −854.000 | −0.0281377 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2375.00 | 0.0780112 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7874.00 | 0.257842 | 0.128921 | − | 0.991655i | \(-0.458849\pi\) | ||||
0.128921 | + | 0.991655i | \(0.458849\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27456.0 | 0.896320 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 690.000 | 0.0224567 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47585.0 | 1.54397 | 0.771987 | − | 0.635639i | \(-0.219263\pi\) | ||||
0.771987 | + | 0.635639i | \(0.219263\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13460.0 | −0.435402 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15015.0 | −0.484228 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16020.0 | 0.515072 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42016.0 | 1.34680 | 0.673402 | − | 0.739277i | \(-0.264832\pi\) | ||||
0.673402 | + | 0.739277i | \(0.264832\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27020.0 | −0.863498 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13200.0 | 0.420571 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1867.00 | −0.0593064 | −0.0296532 | − | 0.999560i | \(-0.509440\pi\) | ||||
−0.0296532 | + | 0.999560i | \(0.509440\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6670.00 | 0.211241 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2240.4.a.be.1.1 | 1 | ||
4.3 | odd | 2 | 2240.4.a.j.1.1 | 1 | |||
8.3 | odd | 2 | 280.4.a.c.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 560.4.a.e.1.1 | 1 | |||
40.3 | even | 4 | 1400.4.g.c.449.2 | 2 | |||
40.19 | odd | 2 | 1400.4.a.d.1.1 | 1 | |||
40.27 | even | 4 | 1400.4.g.c.449.1 | 2 | |||
56.27 | even | 2 | 1960.4.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.4.a.c.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
560.4.a.e.1.1 | 1 | 8.5 | even | 2 | |||
1400.4.a.d.1.1 | 1 | 40.19 | odd | 2 | |||
1400.4.g.c.449.1 | 2 | 40.27 | even | 4 | |||
1400.4.g.c.449.2 | 2 | 40.3 | even | 4 | |||
1960.4.a.d.1.1 | 1 | 56.27 | even | 2 | |||
2240.4.a.j.1.1 | 1 | 4.3 | odd | 2 | |||
2240.4.a.be.1.1 | 1 | 1.1 | even | 1 | trivial |